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  1. ๊ฒฝ๋ถ๋Œ€ํ•™๊ต ํ† ๋ชฉ๊ณตํ•™๊ณผ ๊ต์ˆ˜ (Professor, Department of Civil Engineering, Kyungpook National University, Daegu 41566, Rep. of Korea)
  2. ๊ฒฝ๋ถ๊ฐœ๋ฐœ๊ณต์‚ฌ ๋„์‹œ์žฌ์ƒํŒŒํŠธ ๋ถ€์žฅ (Department Head, Urban Regeneration Part, Kyungpook Development Corporation, Yeacheon 36849, Rep. of Korea)



์ฒ ๊ทผ์ฝ˜ํฌ๋ฆฌํŠธ, 4-ํŒŒ์ผ ์บก, 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ, ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ, ์œ ํšจ๊ฐ•๋„
reinforced concrete, four-pile cap, three-dimensional strut-and-tie model, concrete strut, effective strength

1. ์„œ๋ก 

์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ ๋ฐฉ๋ฒ•์€ ๋ณต์žกํ•œ ํ•˜์ค‘์กฐ๊ฑด ๋ฐ ๊ธฐํ•˜ํ•™์  ํ˜•์ƒ์„ ๊ฐ–๋Š” ์ฝ˜ํฌ๋ฆฌํŠธ ๊ตฌ์กฐ๋ถ€์žฌ ๋ฐ ๊ตฌ์กฐ๋ฌผ์˜ ์„ค๊ณ„์— ํšจ๊ณผ์ ์ด๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ์ด ๋ฐฉ๋ฒ•์„ ์ฝ˜ํฌ๋ฆฌํŠธ ๊ตฌ์กฐ๋ถ€์žฌ์˜ ๊ทนํ•œ๊ฐ•๋„ ํ•ด์„ ๋ฐ ์„ค๊ณ„์— ์ ์šฉํ•˜๊ธฐ ์œ„ํ•ด์„œ๋Š” ์„ ์ •ํ•œ ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ์˜ ์ ํ•ฉ์„ฑ ํŒ๋‹จ ๋ฐ ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ ๊ตฌ์„ฑ์š”์†Œ์˜ ๊ฐ•๋„์กฐ๊ฑด ๊ฒ€ํ† ์— ํ•„์š”ํ•œ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„๋ฅผ ์ •ํ™•ํ•˜๊ฒŒ ๊ฒฐ์ •ํ•ด์•ผ ํ•œ๋‹ค. ํ˜„์žฌ๊นŒ์ง€ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„๋ฅผ ๊ฒฐ์ •ํ•˜๊ธฐ ์œ„ํ•œ ๋งŽ์€ ์‹คํ—˜ ๋ฐ ํ•ด์„์  ์—ฐ๊ตฌ๊ฐ€ ์ง„ํ–‰๋˜์—ˆ๊ณ (Thulimann 1976[28]; Nielsen et al. 1978[19]; Ramirez and Breen 1983[21]; Marti 1985[18]; Schlaich et al. 1987[23]; MacGregor 1988[16], 1997[17]; Bergmeister et al. 1991[6], 1993[7]; Alshegeir 1992[3]; Ha and Hong 2005[13]; Kim et al. 2011[14]; Chae et al. 2011[9]), ์—ฌ๋Ÿฌ ์ข…๋ฅ˜์˜ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ ์œ ํšจ๊ฐ•๋„ ์‹๋“ค์ด ์„ธ๊ณ„ ์ฃผ์š” ์„ค๊ณ„๊ธฐ์ค€์„œ์— ์ฑ„ํƒ๋˜์—ˆ๋‹ค(EC2 2004[12]; FIB 2010[11]; ACI 318 2014[5]; AASHTO 2018[4]). ๊ทธ๋Ÿฌ๋‚˜ ํ˜„ํ–‰ ์„ค๊ณ„๊ธฐ์ค€์˜ ์œ ํšจ๊ฐ•๋„ ์‹๋“ค์€ 2์ฐจ์› ์„ค๊ณ„์˜์—ญ์˜ ์‹คํ—˜ ๋ฐ ํ•ด์„์— ๊ทผ๊ฑฐํ•œ ๋ช‡๋ช‡์˜ ํŠน์ •ํ•œ ๊ฐ’์œผ๋กœ ํ‘œํ˜„๋˜๋ฏ€๋กœ, ์ด๋ฅผ 3์ฐจ์› ์‘๋ ฅ๊ต๋ž€์˜์—ญ์„ ๊ฐ–๋Š” ํŒŒ์ผ์บก์˜ ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ ์„ค๊ณ„์— ์ ์šฉํ•˜๋Š” ๊ฒƒ์€ ์ ์ ˆํ•˜์ง€ ์•Š๋‹ค. ๋”ฐ๋ผ์„œ ํŒŒ์ผ์บก์— ๋Œ€ํ•œ 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ ์„ค๊ณ„๋ฅผ ์ˆ˜ํ–‰ํ•˜๊ธฐ ์œ„ํ•ด์„œ๋Š” 3์ถ• ์‘๋ ฅ์กฐํ•ฉ์˜ ์˜ํ–ฅ ๋ฐ ์ฒ ๊ทผ๋ฐฐ์น˜์˜ ์˜ํ–ฅ์„ ๊ณ ๋ คํ•˜์—ฌ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„๋ฅผ ํ•ฉ๋ฆฌ์ ์ธ ๋ฐฉ๋ฒ•์œผ๋กœ ๊ฒฐ์ •ํ•ด์•ผ ํ•œ๋‹ค.

์ด๋Ÿฌํ•œ ๋ฌธ์ œ๋ฅผ ํ•ด๊ฒฐํ•˜๊ธฐ ์œ„ํ•˜์—ฌ ๋ณธ ์ €์ž๋Š” ์ˆ˜์น˜ํ•ด์„๊ธฐ๋ฒ•์„ ํ™œ์šฉํ•˜๋Š” 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ๊ฒฐ์ •๋ฐฉ๋ฒ•์„ ์ตœ๊ทผ์— ์ œ์•ˆํ•˜์˜€๋‹ค(Yun and Ramirez 2016[31]). ์ œ์•ˆํ•œ ๋ฐฉ๋ฒ•์€ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์ด ์œ„์น˜ํ•œ ๊ณณ์˜ ์‘๋ ฅ ๋ฐ ๋ณ€ํ˜•๋ฅ  ์ƒํƒœ, ์ŠคํŠธ๋Ÿฟ ๊ธธ์ด์˜ ์˜ํ–ฅ, ์ŠคํŠธ๋Ÿฟ๊ณผ ์••์ถ•์ฃผ์‘๋ ฅ ํ๋ฆ„๊ณผ์˜ ๋ถˆ์ผ์น˜์˜ ์˜ํ–ฅ, ์ฝ˜ํฌ๋ฆฌํŠธ ์••์ถ•๊ฐ•๋„์˜ ์˜ํ–ฅ, ๊ทธ๋ฆฌ๊ณ  ์ฒ ๊ทผ์— ์˜ํ•œ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ๊ตฌ์†์˜ ์ •๋„ ๋“ฑ์„ ๊ณ ๋ คํ•˜์—ฌ 3์ฐจ์› ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„๋ฅผ ์ •ํ™•ํ•˜๊ณ  ์ผ๊ด€์„ฑ ์žˆ๊ฒŒ ๊ฒฐ์ •ํ•  ์ˆ˜ ์žˆ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ์ œ์•ˆํ•œ ๋ฐฉ๋ฒ•์€ ํ•˜๋‚˜์˜ ์„ค๊ณ„ํ•˜์ค‘ ์กฐ๊ฑด์— ๋Œ€ํ•ด์„œ๋„ ์ˆ˜์ฐจ๋ก€์˜ ๋ฐ˜๋ณต์ ์ธ 3์ฐจ์› ๊ณ ์ฒด ๋ฐ ํŠธ๋Ÿฌ์Šค์˜ ์œ ํ•œ์š”์†Œํ•ด์„ ๊ณผ์ •๊ณผ ์œ ํ•œ์š”์†Œํ•ด์„ ๊ฒฐ๊ณผ๋ฅผ ์‘์šฉํ•œ ๋ณต์žกํ•œ ์ˆ˜์น˜์ฒ˜๋ฆฌ ๊ณผ์ •์„ ๊ฑฐ์ณ์•ผํ•˜๋Š” ๋‹จ์ ์ด ์žˆ์–ด ์ œ์•ˆํ•œ ๋ฐฉ๋ฒ•์„ ์œ„ํ•œ ์ „๋ฌธ์ ์ธ ํ”„๋กœ๊ทธ๋žจ์„ ํ™œ์šฉํ•˜์ง€ ์•Š๋Š”๋‹ค๋ฉด ๊ทธ ์ ์šฉ์ด ๋งค์šฐ ์–ด๋ ต๋‹ค. ๋”ฐ๋ผ์„œ ์ด ์—ฐ๊ตฌ์—์„œ๋Š” ์ œ์•ˆํ•œ ์ˆ˜์น˜ํ•ด์„์  ๋ฐฉ๋ฒ•์— ๊ทผ๊ฑฐํ•˜์—ฌ ๊ธฐ๋‘ฅ์˜ ์ถ•ํ•˜์ค‘์ด ์ง€๋ฐฐ์ ์ธ ๋‹ค์–‘ํ•œ ์„ค๊ณ„์กฐ๊ฑด์„ ๊ฐ–๋Š” Four-pile Cap์˜ ์‹ค์šฉ์ ์ด๊ณ  ํšจ๊ณผ์ ์ธ 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ ํ•ด์„/์„ค๊ณ„๋ฅผ ์œ„ํ•œ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ์‹์„ ๊ฐœ๋ฐœ, ์ œ์•ˆํ•˜์˜€๋‹ค. ์ด ์—ฐ๊ตฌ์—์„œ ์ œ์•ˆํ•œ ์œ ํšจ๊ฐ•๋„ ์‹๊ณผ ํ˜„ํ–‰ ์„ค๊ณ„๊ธฐ์ค€์˜ ์œ ํšจ๊ฐ•๋„ ์‹๋“ค์„ 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ ํ•ด์„์— ์ ์šฉํ•˜์—ฌ ํŒŒ๊ดด์‹คํ—˜์ด ์ˆ˜ํ–‰๋œ 115๊ฐœ ํŒŒ์ผ์บก ์‹œํ—˜์ฒด์˜ ํŒŒ๊ดด๊ฐ•๋„๋ฅผ ์˜ˆ์ธกํ•˜์˜€์œผ๋ฉฐ, ๊ทธ ๊ฒฐ๊ณผ์˜ ๋น„๊ต๋ถ„์„์„ ํ†ตํ•ด ์ œ์•ˆํ•œ ์ŠคํŠธ๋Ÿฟ ์œ ํšจ๊ฐ•๋„ ์‹์˜ ์ ํ•ฉ์„ฑ์„ ๊ฒ€์ฆํ•˜์˜€๋‹ค.

2. Four-pile Cap์˜ 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ ๋ฐ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„

2.1 ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ

์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ์„ ์ด์šฉํ•œ ์ฒ ๊ทผ์ฝ˜ํฌ๋ฆฌํŠธ Four- pile Cap์˜ ์„ค๊ณ„๋Š” ์ผ๋ฐ˜์ ์œผ๋กœ Fig. 1(a)์™€ ๊ฐ™์€ ์ •์ • ํŠธ๋Ÿฌ์Šค ๊ตฌ์กฐ์˜ 8์ ˆ์  3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ์„ ์ด์šฉํ•˜์—ฌ ์ˆ˜ํ–‰ํ•  ์ˆ˜ ์žˆ๋‹ค(ACI 445 2002[1], PCA 2004[20]). ๊ทธ๋Ÿฌ๋‚˜ Fig. 1(a)์˜ ๋ชจ๋ธ์€ ํŒŒ์ผ์บก ํ•˜๋‹จ์˜ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์ธ์žฅ์ €ํ•ญ ๊ธฐ๋Šฅ์ด ์™„์ „ํžˆ ๋ฌด์‹œ๋˜์–ด Four-pile Cap์˜ ์‹คํ—˜ ์‹œ์˜ ํŒŒ๊ดด๋ชจ๋“œ๋ฅผ ๋ถ€์ •ํ™•ํ•˜๊ฒŒ ์˜ˆ์ธกํ•˜๋ฉฐ ํŒŒ๊ดด๊ฐ•๋„๋ฅผ ์ง€๋‚˜์น˜๊ฒŒ ๋‚ฎ๊ฒŒ ํ‰๊ฐ€ํ•˜์—ฌ ๋งค์šฐ ๋ณด์ˆ˜์ ์ธ ํŒŒ์ผ์บก ์„ค๊ณ„ ๊ฒฐ๊ณผ๋ฅผ ์ดˆ๋ž˜ํ•˜๋Š” ๊ฒƒ์œผ๋กœ ํŒ๋ช…๋˜์—ˆ๋‹ค(Kim et al. 2013[15]). ๋”ฐ๋ผ์„œ ์ด ์—ฐ๊ตฌ์—์„œ๋Š” Kim et al.(2013)[15]์ด ์ œ์•ˆํ•œ Fig. 1(b)์™€ ๊ฐ™์€ ๋ถ€์ •์ • ํŠธ๋Ÿฌ์Šค ๊ตฌ์กฐ์˜ 8์ ˆ์  3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ์„ ๊ธฐ๋‘ฅ์˜ ์ˆ˜์งํ•˜์ค‘์ด ์ง€๋ฐฐ์ ์ธ Four-pile Cap์˜ ๋ชจ๋ธ๋กœ ์ฑ„ํƒํ•˜์˜€๋‹ค.

Fig. 1. Three-dimensional strut-and-tie model for four-pile cap

../../Resources/kci/JKCI.2019.31.1.049/fig1.png

2.2 ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„

EC2(2004)[12]๋Š” ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ์‹์„ ์‹ค๋ฆฐ๋” ์••์ถ•๊ฐ•๋„์˜ ์„ค๊ณ„ ๊ฐ’ $f_ {cd}$(=$\alpha_{c c} f_{c k} / \gamma_{c}$, $\alpha_{c c}$= ์‹œ๊ฐ„์— ๋”ฐ๋ฅธ ์ฝ˜ํฌ๋ฆฌํŠธ ๊ฐ•๋„์˜ ๋ณ€ํ™”๋ฅผ ๊ณ ๋ คํ•˜๋Š” ๊ณ„์ˆ˜, $\gamma_{c}$= ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๋ถ€๋ถ„์•ˆ์ „ ๊ณ„์ˆ˜)๋ฅผ ์‚ฌ์šฉํ•˜์—ฌ ๋‹ค์Œ๊ณผ ๊ฐ™์ด ์ œ์‹œํ•˜์˜€๋‹ค

(1)
$f_{ce, s}=\alpha_{e} f_{cd}$

์—ฌ๊ธฐ์„œ, $\alpha_{e}$๋Š” ์œ ํšจ๊ฐ•๋„๊ณ„์ˆ˜๋กœ์„œ ์ŠคํŠธ๋Ÿฟ ์ถ•์˜ ์ง๊ฐ๋ฐฉํ–ฅ์œผ๋กœ ์ธ์žฅ์‘๋ ฅ์ด ์—†์„ ๊ฒฝ์šฐ๋Š” 1.0์„, ์žˆ์„ ๊ฒฝ์šฐ๋Š” 0.6$\left(1-f_{c k} / 250\right)$์ด๋‹ค. ์‹ (1)์—์„œ, $f_{ce, s}$์˜ ๋‹จ์œ„๋Š” MPa์ด๋‹ค.

FIB(2010)[11]๋Š” ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ์‹์„ ๋‹ค์Œ๊ณผ ๊ฐ™์ด ์ œ์‹œํ•˜์˜€๋‹ค.

(2)
$f_{c e, s}=\alpha_{f}\left(30 / f_{c k}\right)^{1 / 3} f_{cd}$

์—ฌ๊ธฐ์„œ, $\alpha_{f}$๋Š” ๊ฐ•๋„๊ฐ์†Œ๊ณ„์ˆ˜๋กœ์„œ, ๊ต๋ž€๋˜์ง€ ์•Š๋Š” 1์ถ• ์••์ถ•์‘๋ ฅ ๋˜๋Š” 2์ถ• ์••์ถ•์‘๋ ฅ์„ ๋ฐ›๋Š” ์ŠคํŠธ๋Ÿฟ์˜ ๊ฒฝ์šฐ๋Š” 1.0, ์ŠคํŠธ๋Ÿฟ์˜ ์ถ•๋ฐฉํ–ฅ๊ณผ ํ‰ํ–‰ํ•˜๊ฒŒ ๊ท ์—ด์ด ๋ฐœ์ƒํ•˜๊ณ  ๊ท ์—ด ์ง๊ฐ๋ฐฉํ–ฅ์œผ๋กœ ์ธ์žฅ์„ ๋ฐ›๋Š” ์ฒ ๊ทผ์ด ์žˆ๋Š” ์ŠคํŠธ๋Ÿฟ์˜ ๊ฒฝ์šฐ๋Š” 0.75, ๊ทธ๋ฆฌ๊ณ  ์ŠคํŠธ๋Ÿฟ์˜ ์ถ•๋ฐฉํ–ฅ๊ณผ ๋น„์Šค๋“ฌํ•œ ๋ฐฉํ–ฅ์œผ๋กœ ์ฒ ๊ทผ์ด ์žˆ๋Š” ์ŠคํŠธ๋Ÿฟ์˜ ๊ฒฝ์šฐ๋Š” 0.55์ด๋‹ค. ์ด ์„ค๊ณ„๊ธฐ์ค€์€ $\alpha_{f}\left(30 / f_{c k}\right)^{1 / 3}$์˜ ๊ฐ’์„ ์ƒ๊ธฐ์˜ ๊ฐ ๊ฒฝ์šฐ์— ๋Œ€ํ•˜์—ฌ 1.0, 0.8, 0.55๋กœ ์ œํ•œํ•˜๊ณ  ์žˆ๋‹ค.

AASHTO(2018)[4]๋Š” ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ์‹์„ Vecchio and Collins(1982)[29]์˜ ์—ฐ๊ตฌ๊ฒฐ๊ณผ๋ฅผ ๋ฐ˜์˜ํ•˜์—ฌ ์‹ (3)๊ณผ ๊ฐ™์ด ์ œ์‹œํ•˜์˜€๋‹ค. Vecchio and Collins[29]๋Š” ๊ท ์ผํ•œ ์‘๋ ฅ๊ณผ ๋ณ€ํ˜•์„ ๊ฒช๋Š” ์ฝ˜ํฌ๋ฆฌํŠธ ํŒจ๋„์˜ ์‹œํ—˜๊ฒฐ๊ณผ์— ๊ทผ๊ฑฐํ•˜์—ฌ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ์‹์„ ์œ ๋„ํ•˜์˜€๋Š”๋ฐ, ์ด ์‹์€ ์ŠคํŠธ๋Ÿฟ์— ํ‰ํ–‰ํ•œ ๊ท ์—ด๋“ค์„ ์„ค๋ช…ํ•˜๋Š” ๊ฒฝํ—˜์  ์ƒ์ˆ˜๋ฅผ ํฌํ•จํ•˜๊ณ  ์žˆ๋‹ค. CSA(2014)[8]์—์„œ๋Š” ๊ทธ๋“ค์˜ ์‹์„ ์•ฝ๊ฐ„ ๋‹จ์ˆœํ™”ํ•˜์—ฌ ์‹ (3)์„ ์ฑ„ํƒํ•˜์˜€์œผ๋ฉฐ, AASHTO[4]๋Š” ์‹ (3)์˜ ์ตœ๋Œ€๊ฐ’์„ $0.85 f_{c k}$์œผ๋กœ ์ œํ•œํ•˜์˜€๋‹ค.

(3)
$f_{c e, s}=\frac{f_{c k}}{0.8+170 \epsilon_{1}}$

์—ฌ๊ธฐ์„œ, $f_{c e, s}$์˜ ๋‹จ์œ„๋Š” MPa์ด๋ฉฐ, $\epsilon_{1}$์€ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์— ์ˆ˜์ง์œผ๋กœ ๋ฐฐ๊ทผ๋œ ์ฒ ๊ทผ์˜ ํ‰๊ท  ์ธ์žฅ๋ณ€ํ˜•๋ฅ ์ด๋‹ค. ์ผ๋ฐ˜์ ์œผ๋กœ ๋งŽ์€ D-์˜์—ญ(์‘๋ ฅ๊ต๋ž€์˜์—ญ)์—์„œ $\epsilon_{1}$์„ ์ถ”์ •ํ•˜๋Š” ํ•ฉ๋ฆฌ์ ์ธ ๋ฐฉ๋ฒ•์ด ์—†๊ธฐ์— $\epsilon_{1}$์„ ์ฒ ๊ทผ์˜ ์ธ์žฅ๋ณ€ํ˜•๋ฅ ์˜ ํ•จ์ˆ˜๋กœ ๋‹ค์Œ๊ณผ ๊ฐ™์ด ์ œ์‹œํ•˜์˜€๋‹ค.

(4)
$\epsilon_{1}=\epsilon_{s}+\left(\epsilon_{s}+0.002\right) \cot ^{2} \alpha_{s}$

์—ฌ๊ธฐ์„œ, $\epsilon_{s}$๋Š” ์ŠคํŠธ๋Ÿฟ ์ถ•์—์„œ $\alpha_{s}$์˜ ๊ฐ๋„๋กœ ์ŠคํŠธ๋Ÿฟ์„ ๊ฐ€๋กœ์ง€๋ฅด๋Š” ์ฒ ๊ทผ์˜ ํ‰๊ท  ์ธ์žฅ๋ณ€ํ˜•๋ฅ ๋กœ์„œ, ์„ค๊ณ„๊ธฐ์ค€์„œ๋Š” $\epsilon_{s}$๋ฅผ ์ฒ ๊ทผ์˜ ํ•ญ๋ณต๋ณ€ํ˜•๋ฅ ๋กœ ์ œ์‹œํ•˜์˜€๋‹ค.

ACI 318(2014)[5]์€ ์ŠคํŠธ๋Ÿฟ ์ค‘๊ฐ„์ง€์ ์˜ ๋‹จ๋ฉดํ˜•์ƒ๊ณผ ์ŠคํŠธ๋Ÿฟ ์–‘๋‹จ์˜ ๋‹จ๋ฉดํ˜•์ƒ๊ณผ์˜ ๊ด€๊ณ„์™€ ๋ฐฐ์น˜ํ•˜๋Š” ์ฒ ๊ทผ๋Ÿ‰ ๋“ฑ์„ ๊ณ ๋ คํ•˜์—ฌ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ์‹์„ ๋‹ค์Œ๊ณผ ๊ฐ™์ด ์ œ์•ˆํ•˜์˜€๋‹ค.

(5)
$f_{c e, s}=0.85 \beta_{s} f_{c k}$

์—ฌ๊ธฐ์„œ, $\beta_{s}$๋Š” ๊ท ์—ด ๋ฐ ๊ตฌ์†์ฒ ๊ทผ์ด ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„์— ๋ฏธ์น˜๋Š” ์˜ํ–ฅ์„ ๊ณ ๋ คํ•˜๊ธฐ ์œ„ํ•œ ๊ณ„์ˆ˜๋กœ์„œ, ์ŠคํŠธ๋Ÿฟ ์ค‘๊ฐ„์ง€์ ์˜ ๋‹จ๋ฉด์ ์ด ์ŠคํŠธ๋Ÿฟ ์–‘๋‹จ์˜ ๋‹จ๋ฉด์ ๊ณผ ๊ฐ™์„ ๋•Œ๋Š” 1.0, ์ŠคํŠธ๋Ÿฟ ์ค‘๊ฐ„์ง€์ ์˜ ๋‹จ๋ฉด์ ์ด ์ŠคํŠธ๋Ÿฟ ์–‘๋‹จ์˜ ๋‹จ๋ฉด์ ๋ณด๋‹ค ํฌ๊ณ  ์ŠคํŠธ๋Ÿฟ์„ ๊ฐ€๋กœ์ง€๋ฅด๋Š” ์ธ์žฅ์ฒ ๊ทผ์˜ ์‘๋ ฅ ๋ฐ ๋ฐฐ์น˜์— ๊ด€ํ•œ ACI 318 ์„ค๊ณ„๊ธฐ์ค€์˜ ์กฐ๊ฑด์‹(23.5.3)์„ ๋งŒ์กฑํ•  ๊ฒฝ์šฐ๋Š” 0.75, ๊ทธ๋ฆฌ๊ณ  ์ŠคํŠธ๋Ÿฟ ์ค‘๊ฐ„์ง€์ ์˜ ๋‹จ๋ฉด์ ์ด ์ŠคํŠธ๋Ÿฟ ์–‘๋‹จ์˜ ๋‹จ๋ฉด์ ๋ณด๋‹ค ํฌ๊ณ  ์ธ์žฅ์ฒ ๊ทผ์˜ ์‘๋ ฅ ๋ฐ ๋ฐฐ์น˜์— ๊ด€ํ•œ ์กฐ๊ฑด์‹(23.5.3)์„ ๋งŒ์กฑํ•˜์ง€ ๋ชปํ•  ๊ฒฝ์šฐ๋Š” 0.65$\lambda$(์—ฌ๊ธฐ์„œ $\lambda$๋Š” ์ผ๋ฐ˜์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๊ฒฝ์šฐ 1.0, sand-๊ฒฝ๋Ÿ‰์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๊ฒฝ์šฐ 0.85, ๊ฒฝ๋Ÿ‰์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๊ฒฝ์šฐ 0.75)์˜ ๊ฐ’์„ ๊ฐ–๋Š”๋‹ค.

์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ๊ฐ’์€ ์ŠคํŠธ๋Ÿฟ์ด ์œ„์น˜ํ•œ ๊ณณ์˜ ์‘๋ ฅ ์ƒํƒœ ๋ฐ ์ŠคํŠธ๋Ÿฟ์„ ๊ฐ€๋กœ์ง€๋ฅด๋Š” ์ฒ ๊ทผ์˜ ๋ณ€ํ˜•๋ฅ  ์ƒํƒœ์— ํฌ๊ฒŒ ์ขŒ์šฐ๋œ๋‹ค. D-์˜์—ญ์˜ ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ ํ•ด์„/์„ค๊ณ„ ์‹œ ์ด๋“ค์˜ ์˜ํ–ฅ์„ ์ •ํ™•ํ•˜๊ฒŒ ํŒŒ์•…ํ•˜์—ฌ ๋ฐ˜์˜ํ•  ์ˆ˜ ์žˆ๋Š” ์„ค๊ณ„๊ธฐ์ค€์„ ์ œ์•ˆํ•˜๋Š” ๊ฒƒ์€ ๋งค์šฐ ์–ด๋ ต๋‹ค. ์ด๋Ÿฌํ•œ ์ด์œ ๋กœ ์•ž์„œ ์†Œ๊ฐœํ•œ EC2, FIB, ACI 318 ๋“ฑ์˜ ์„ค๊ณ„๊ธฐ์ค€์€ ๋ช‡ ๊ฐ€์ง€ ์ œํ•œ๋œ ๊ฒฝ์šฐ์— ๋Œ€ํ•˜์—ฌ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ๊ฐ’์„ ๊ฒฐ์ •ํ•  ์ˆ˜ ์žˆ๋Š” ์‹์„ ์ œ์•ˆํ•˜์˜€์œผ๋ฉฐ, AASHTO๋Š” ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„๋ฅผ(์ˆ˜์ฐจ๋ก€์˜ ๋ฐ˜๋ณต์ ์ธ ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ ์„ค๊ณ„๋ฅผ ํ†ตํ•ด ์‚ฐ์ •ํ•ด์•ผํ•˜๋Š”) ์ŠคํŠธ๋Ÿฟ์„ ๊ฐ€๋กœ์ง€๋ฅด๋Š” ์ฒ ๊ทผ์˜ ๋ณ€ํ˜•๋ฅ ์˜ ํ•จ์ˆ˜๋กœ ๊ตญํ•œ์‹œ์ผœ ์ œ์•ˆํ•˜์˜€๋‹ค. ๋ฌด์—‡๋ณด๋‹ค ํ˜„ํ–‰ ์„ค๊ณ„๊ธฐ์ค€์˜ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ์‹์€ 2์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ ํ•ด์„/์„ค๊ณ„์— ์ ์šฉํ•  ์ˆ˜ ์žˆ๋Š” ๊ฒƒ์œผ๋กœ, 3์ฐจ์› ์ฝ˜ํฌ๋ฆฌํŠธ ๊ตฌ์กฐ๋ถ€์žฌ์˜ ํ•ด์„/์„ค๊ณ„์— ์ ์šฉํ•˜๋Š” ๊ฒƒ์€ ์ ์ ˆํ•˜์ง€ ์•Š๋‹ค. ์ด๋Ÿฌํ•œ ๋ฌธ์ œ๋ฅผ ํ•ด๊ฒฐํ•˜๊ณ ์ž Yun and Ramirez(2016)[31]๋Š” ์ˆ˜์น˜ํ•ด์„์ ์ธ ๊ธฐ๋ฒ•์„ ํ™œ์šฉํ•˜์—ฌ 3์ฐจ์› ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„๋ฅผ ๊ฒฐ์ •ํ•˜๋Š” ๋ฐฉ๋ฒ•์„ ์ œ์•ˆํ•˜์˜€๋‹ค. ์ œ์•ˆํ•œ ๋ฐฉ๋ฒ•์„ ๋‹จ๊ณ„๋ณ„๋กœ ๊ฐ„๋‹จํžˆ ์„ค๋ช…ํ•˜๋ฉด ๋‹ค์Œ๊ณผ ๊ฐ™๋‹ค. ๋‹จ๊ณ„ 1: ํ•ด์„ ๋˜๋Š” ์„ค๊ณ„ ๋Œ€์ƒ ์˜์—ญ์˜ 3์ฐจ์› ๋ฌด๊ทผ์ฝ˜ํฌ๋ฆฌํŠธ ์œ ํ•œ์š”์†Œํ•ด์„ ๋ชจ๋ธ์—์„œ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์ข…์ถ•๊ณผ ๋งŒ๋‚˜๋Š” ์œ ํ•œ์š”์†Œ๋“ค์„ ์„ ์ •ํ•œ๋‹ค. ๋‹จ๊ณ„ 2: 3์ฐจ์› ๋ฌด๊ทผ์ฝ˜ํฌ๋ฆฌํŠธ ์œ ํ•œ์š”์†Œํ•ด์„ ๋ชจ๋ธ์— ๋Œ€ํ•œ ์„ ํ˜•ํƒ„์„ฑ ์œ ํ•œ์š”์†Œํ•ด์„์„ ์ˆ˜ํ–‰ํ•˜์—ฌ ๋‹จ๊ณ„ 1์—์„œ ์„ ์ •ํ•œ ๊ฐ ์ฝ˜ํฌ๋ฆฌํŠธ ์œ ํ•œ์š”์†Œ์˜ ์ฃผ์‘๋ ฅ์˜ ํฌ๊ธฐ $\sigma_{i}(i=1,2,3)\left(\sigma_{1} \leq \sigma_{2} \leq \sigma_{3}\right)$๋ฅผ ๊ฒฐ์ •ํ•œ๋‹ค. ๋˜ํ•œ Willam and Warnke(1974)[30]์˜ 5๊ณ„์ˆ˜ ํฌ๋ฝ์„ ์œผ๋กœ ํ‘œํ˜„๋˜๋Š” 3์ฐจ์› ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ํŒŒ๊ดด๊ธฐ์ค€์„ ์ ์šฉํ•˜์—ฌ ํŒŒ๊ดด ํฌ๋ฝ๋ฉด ์ƒ์˜ ์ฃผ์‘๋ ฅ $\sigma_{1f}$(์ตœ๋Œ€์••์ถ•์ฃผ์‘๋ ฅ), $\sigma_{2f}$, $\sigma_{3f}$๋ฅผ ๊ฒฐ์ •ํ•œ๋‹ค. ๋‹จ๊ณ„ 3: ์ฝ˜ํฌ๋ฆฌํŠธ ์œ ํ•œ์š”์†Œ $e$์˜ ์ฃผ์‘๋ ฅ $\sigma_{1}$์˜ ์ž‘์šฉ๋ฐฉํ–ฅ๊ณผ ์ŠคํŠธ๋Ÿฟ์˜ ์ข…์ถ•๋ฐฉํ–ฅ์ด ๋™์ผํ•œ ๊ฒฝ์šฐ ๋‹จ๊ณ„ 2์—์„œ ๊ฒฐ์ •ํ•œ ์ฝ˜ํฌ๋ฆฌํŠธ ์œ ํ•œ์š”์†Œ์˜ ํŒŒ๊ดดํฌ๋ฝ๋ฉด ์ƒ์˜ ์ตœ๋Œ€์••์ถ•์ฃผ์‘๋ ฅ $\sigma_{1f}$๋ฅผ ์ฝ˜ํฌ๋ฆฌํŠธ ์œ ํ•œ์š”์†Œ $e$์˜ ์ŠคํŠธ๋Ÿฟ ์ข…์ถ•๋ฐฉํ–ฅ์˜ ์œ ํšจ๊ฐ•๋„ $f_{ce,s(ele)}$๋กœ ์ทจํ•œ๋‹ค. ์ฝ˜ํฌ๋ฆฌํŠธ ์œ ํ•œ์š”์†Œ $e$์˜ ์ฃผ์‘๋ ฅ $\sigma_{1}$์˜ ์ž‘์šฉ๋ฐฉํ–ฅ๊ณผ ์ŠคํŠธ๋Ÿฟ์˜ ์ข…์ถ•๋ฐฉํ–ฅ์ด ๋™์ผํ•˜์ง€ ์•Š์„ ๊ฒฝ์šฐ, $\sigma_{1f}$๋ฅผ ๋‹ค์Œ์˜ ๋ฐฉํ–ฅ์ฝ”์‚ฌ์ธํ–‰๋ ฌ์„ ์ด์šฉํ•œ ์‘๋ ฅ๋ณ€ํ™˜์‹ (6)์„ ์ด์šฉํ•˜์—ฌ ์ˆ˜์ •ํ•œ๋‹ค. ์ด๋Ÿฌํ•œ ๋ณด์ •์€ ์„ค๊ณ„์˜์—ญ์˜ ์••์ถ•์ฃผ์‘๋ ฅ $\sigma_{1f}$์˜ ์ž‘์šฉ๋ฐฉํ–ฅ๊ณผ ์ŠคํŠธ๋Ÿฟ ์ข…์ถ•๋ฐฉํ–ฅ์ด ๋‹ค๋ฅผ ๊ฒฝ์šฐ ์ŠคํŠธ๋Ÿฟ์˜ ํ•˜์ค‘์ „๋‹ฌ๋Šฅ๋ ฅ์ด ๊ฐ์†Œ๋˜๋Š” ๊ฒƒ์„ ๊ณ ๋ คํ•˜๊ธฐ ์œ„ํ•จ์ด๋‹ค.

(6)
$\left[ \begin{array}{ccc}{f_{c s, e}} & {f_{12}} & {f_{13}} \\ {f_{21}} & {f_{22}} & {f_{23}} \\ {f_{31}} & {f_{32}} & {f_{33}}\end{array}\right]=\left[T_{s}\right]\left[T_{p}^{T}\right] \left[ \begin{array}{ccc}{\sigma_{1 f}} & {0} & {0} \\ {0} & {\sigma_{2 f}} & {0} \\ {0} & {0} & {\sigma_{3 f}}\end{array}\right]\left[T_{p}\right]\left[T_{s}^{T}\right]$

์—ฌ๊ธฐ์„œ, $\left[T_{s}\right]$๋Š” ์ „์ฒด์ขŒํ‘œ๊ณ„($x$-, $y$-, $z$-์ถ•)์™€ ์ŠคํŠธ๋Ÿฟ์˜ ๊ตญ๋ถ€์ขŒํ‘œ๊ณ„($1s$-, $2s$-, $3s$-์ถ•; $1s$-์ถ•=์ŠคํŠธ๋Ÿฟ์˜ ์ข…์ถ•) ์‚ฌ์ด์˜ ๋ฐฉํ–ฅ์ฝ”์‚ฌ์ธ ํ–‰๋ ฌ์ด๋ฉฐ, $\left[T_{p}\right]$๋Š” ์ „์ฒด์ขŒํ‘œ๊ณ„์™€ ์œ ํ•œ์š”์†Œ์˜ ์ฃผ์‘๋ ฅ ์ขŒํ‘œ๊ณ„($1$-, $2$-, $3$-์ถ•; $1$-์ถ• = ์ฃผ์‘๋ ฅ $\sigma_{1}$์˜ ์ž‘์šฉ๋ฐฉํ–ฅ ์ถ•) ์‚ฌ์ด์˜ ๋ฐฉํ–ฅ์ฝ”์‚ฌ์ธ ํ–‰๋ ฌ์ด๋‹ค. ๋‹จ๊ณ„ 4: ๋‹จ๊ณ„ 3์—์„œ ๊ตฌํ•œ ๊ฐ ์ฝ˜ํฌ๋ฆฌํŠธ ์œ ํ•œ์š”์†Œ์˜ ์ŠคํŠธ๋Ÿฟ ์ข…์ถ•๋ฐฉํ–ฅ ์œ ํšจ๊ฐ•๋„ $f_{ce,s(ele)}$ ์ค‘ ํ‰๊ท ยฑํ‘œ์ค€ํŽธ์ฐจ ๋ฒ”์œ„ ๋‚ด์— ์žˆ๋Š” ์œ ํšจ๊ฐ•๋„ $f_{ce,s}^{*}$๋“ค์˜ ํ‰๊ท ์„ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ $f_{ce,s}$๋กœ ๊ฒฐ์ •ํ•œ๋‹ค. ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ๊ฐ•๋„๋Š” ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์••์ถ•๊ฐ•๋„์˜ ์˜ํ–ฅ์„ ๋ฐ›๋Š”๋‹ค(Bergmeister et al. 1993[7], MacGregor 1997[17]). ๋”ฐ๋ผ์„œ ํ˜„ ๋‹จ๊ณ„์—์„œ ๊ฒฐ์ •ํ•œ $f_{ce,s}$์— $28 < f_{c k} < 70 \mathrm{MPa}$์ผ ๊ฒฝ์šฐ๋Š” ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์••์ถ•๊ฐ•๋„์˜ ์˜ํ–ฅ์„ ๊ณ ๋ คํ•˜๋Š” ๊ณ„์ˆ˜($\nu_{1}$) $1.1-0.25 f_{c k} / 70$๋ฅผ, $f_{d x} \leq 28 \mathrm{MPa}$์ผ ๊ฒฝ์šฐ๋Š” 1.0์„, ๊ทธ๋ฆฌ๊ณ  $f_{c k} \geq 70 \mathrm{MPa}$์ผ ๊ฒฝ์šฐ๋Š” 0.85๋ฅผ ๊ณฑํ•œ๋‹ค. ๋‹จ๊ณ„ 5: ์ฒ ๊ทผ์— ์˜ํ•ด ์ฝ˜ํฌ๋ฆฌํŠธ๊ฐ€ ๊ตฌ์†๋˜๋Š” ํ˜„์ƒ์„ ๊ณ ๋ คํ•˜๊ธฐ ์œ„ํ•ด ์ฒ ๊ทผ ํƒ€์ด์˜ ๋‹จ๋ฉด๋ ฅ์„ ์ฒ ๊ทผ์— ์˜ํ•œ ๊ตฌ์†๋ ฅ์œผ๋กœ ๊ฐ„์ฃผํ•˜๊ณ , ์ด ๊ตฌ์†๋ ฅ์„ 3์ฐจ์› ๋ฌด๊ทผ์ฝ˜ํฌ๋ฆฌํŠธ ์œ ํ•œ์š”์†Œํ•ด์„ ๋ชจ๋ธ์— ์™ธ๋ถ€ํ•˜์ค‘๊ณผ ๋”๋ถˆ์–ด ์ž‘์šฉ์‹œํ‚จ ํ›„ ๋‹จ๊ณ„ 2๋กœ ๋˜๋Œ์•„๊ฐ„๋‹ค. ์ด ๊ณผ์ •์„ ์ „ ๋‹จ๊ณ„ ๋ฐ ํ˜„ ๋‹จ๊ณ„์˜ ์ฒ ๊ทผ ํƒ€์ด์˜ ๋‹จ๋ฉด๋ ฅ์ด ๊ฐ™์•„์งˆ ๋•Œ๊นŒ์ง€ ๋ฐ˜๋ณตํ•œ๋‹ค.

3. ์ŠคํŠธ๋Ÿฟ ์œ ํšจ๊ฐ•๋„ ์‹์˜ ์ œ์•ˆ

Yun and Ramirez(2016)[31]์˜ ์ˆ˜์น˜ํ•ด์„์  ๋ฐฉ๋ฒ•์€ 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„๋ฅผ ๊ธฐํƒ€์˜ ์—ฌ๋Ÿฌ ๋ฐฉ๋ฒ•์— ๋น„ํ•ด ํ•ฉ๋ฆฌ์ ์ด๋ฉฐ ๋…ผ๋ฆฌ์ ์œผ๋กœ ๊ฒฐ์ •ํ•˜๋Š” ๊ฒƒ์œผ๋กœ ํŒ๋ช…๋˜์—ˆ์œผ๋‚˜, ๋ฐ˜๋ณต์ ์ธ 3์ฐจ์› ๊ณ ์ฒด ๋ฐ ํŠธ๋Ÿฌ์Šค ์œ ํ•œ์š”์†Œํ•ด์„ ๊ณผ์ •๊ณผ ์œ ํ•œ์š”์†Œํ•ด์„ ๊ฒฐ๊ณผ๋ฅผ ์‘์šฉํ•œ ๋ณต์žกํ•œ ์ˆ˜์น˜์ฒ˜๋ฆฌ ๊ณผ์ •์„ ๊ฑฐ์ณ์•ผํ•˜๋Š” ๋‹จ์ ์œผ๋กœ ์ธํ•ด ๊ทธ ์ ์šฉ์ด ์–ด๋ ต๋‹ค. ์ด ์—ฐ๊ตฌ์—์„œ๋Š” ๊ทธ๋“ค์˜ ์ˆ˜์น˜ํ•ด์„์  ๋ฐฉ๋ฒ•์„ ์ˆ˜์งํ•˜์ค‘์ด ์ง€๋ฐฐ์ ์ธ ๋ชจ๋“  ํ˜•์ƒ์˜ Four-pile Cap์— ์ ์šฉํ•˜์—ฌ 8์ ˆ์  3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ์˜ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ๊ฐ’์„ ๊ตฌํ•˜์˜€์œผ๋ฉฐ, ๋˜ํ•œ ์‹ค๋ฌด ์ ์šฉ์„ ์œ„ํ•ด ์—ฌ๋Ÿฌ ์„ค๊ณ„์กฐ๊ฑด ์กฐํ•ฉ์— ๋Œ€ํ•ด ๊ฒฐ์ •ํ•œ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ๊ฐ’์œผ๋กœ๋ถ€ํ„ฐ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ์‹์„ ๊ฐœ๋ฐœ, ์ œ์•ˆํ•˜์˜€๋‹ค.

์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ์‹ ๊ฐœ๋ฐœ์„ ์œ„ํ•ด ์‚ฌ์šฉํ•œ Fig. 2์˜ ํŒŒ์ผ์บก ๋ชจ๋ธ์˜ ์ฃผ์š” ์„ค๊ณ„๋ณ€์ˆ˜, ์ฆ‰ ๊ธฐ๋‘ฅ์ „๋ฉด์—์„œ ํŒŒ์ผ์ค‘์‹ฌ๊นŒ์ง€์˜ ๊ฑฐ๋ฆฌ์™€ ํŒŒ์ผ์บก์˜ ์œ ํšจ๊นŠ์ด์˜ ๋น„(์ „๋‹จ๊ฒฝ๊ฐ„๋น„) $w / d$, ๊ธฐ๋‘ฅํญ/์œ ํšจ๊นŠ์ด ๋น„ $c / d$, ๊ทธ๋ฆฌ๊ณ  ๋ฐฐ๊ทผ์ฒ ๊ทผ๋Ÿ‰/ํ•„์š”์ฒ ๊ทผ๋Ÿ‰ ๋น„ $A_ {s,prov} / A_ {s,req}$๋Š” ๊ฐ๊ฐ 0.2-1.0, 0.5-2.0, 0.6-1.0 ๋ฒ”์œ„์ด๋‹ค. Fig. 2์—์„œ ํŒŒ์ผ์บก์˜ ๋‘๊ป˜๋ฅผ 2000 mm๋กœ ๊ณ ์ •ํ•  ๋•Œ ์ƒ๋ถ€ ๊ธฐ๋‘ฅ์˜ ํญ์ด 1000โˆผ4000 mm, ์ „๋‹จ๊ฒฝ๊ฐ„์ด 400โˆผ2000 mm, ๊ทธ๋ฆฌ๊ณ  ํŒŒ์ผ๊ณผ ํŒŒ์ผ ์‚ฌ์ด์˜ ๊ฑฐ๋ฆฌ ์ฆ‰ ํƒ€์ด์˜ ๊ธธ์ด๋Š” 1800โˆผ8000 mm ๋ฒ”์œ„์— ์žˆ๋‹ค. ์ผ๋ฐ˜์ ์œผ๋กœ ์‹ค๋ฌด์—์„œ ์‚ฌ์šฉํ•˜๋Š” ํŒŒ์ผ์˜ ๊ทœ๊ฒฉ์€ ๎‚ฑ508์ด๋ฏ€๋กœ ํŒŒ์ผ์บก์˜ ์ˆ˜์น˜ํ•ด์„ ๋ชจ๋ธ๋ง ์‹œ ํŒŒ์ผ์˜ ์ง๊ฒฝ์„ ํŽธ์˜์ƒ 500 mm๋กœ ๊ฐ„์ฃผํ•˜์˜€๋‹ค. ํŒŒ์ผ์˜ ์ค‘์‹ฌ์—์„œ ์™ธ๋ถ€์ธก๋ฉด๊นŒ์ง€์˜ ๊ฑฐ๋ฆฌ๋Š” 500 mm๋กœ ์ทจํ•˜์˜€์œผ๋ฉฐ, ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ ์ƒ๋ถ€ ๋ฐ ํ•˜๋ถ€ ์ ˆ์ ์—์„œ ์ƒํ•˜๋ถ€ ์™ธ์ธก๋ฉด๊นŒ์ง€์˜ ๊ฑฐ๋ฆฌ๋Š” ํŒŒ์ผ์บก ์œ ํšจ๊นŠ์ด์˜ 10 %๋กœ ์ทจํ•˜์˜€๋‹ค. ์ˆ˜์น˜ํ•ด์„ ์‹œ ํŒŒ์ผ์บก์— 20,000 kN์˜ ๊ธฐ๋‘ฅํ•˜์ค‘์„ ์ž‘์šฉ์‹œ์ผฐ๋‹ค. ํŒŒ์ผ์บก์—๋Š” ์ˆ˜์งํ•˜์ค‘๊ณผ ๊ธฐ๋‘ฅ ์ „๋‹จ๋ ฅ์— ์˜ํ•œ ๋ชจ๋ฉ˜ํŠธ๊ฐ€ ์ž‘์šฉํ•  ์ˆ˜ ์žˆ์œผ๋‚˜, ์ด ์—ฐ๊ตฌ์—์„œ๋Š” ๊ธฐ๋‘ฅ์˜ ์ „๋‹จ๋ ฅ์— ์˜ํ•œ ๋ชจ๋ฉ˜ํŠธ๋Š” ๊ณ ๋ คํ•˜์ง€ ์•Š์•˜๋‹ค.

Fig. 2. Numerical model of four-pile cap for determining effective strength of concrete strut

../../Resources/kci/JKCI.2019.31.1.049/fig2.png

์ฒ ๊ทผ์ฝ˜ํฌ๋ฆฌํŠธ ํŒŒ์ผ์บก์˜ ๊ฐ•๋„ ๋ฐ ๊ฑฐ๋™์— ์˜ํ–ฅ์„ ๋ฏธ์น˜๋Š” ์ฃผ์š” ์„ค๊ณ„๋ณ€์ˆ˜๋ฅผ ๋‹ค์–‘ํ•˜๊ฒŒ ์กฐํ•ฉํ•˜์—ฌ ๋…ผ๋ฌธ 2.2์ ˆ์˜ ๋‹จ๊ณ„ 4์—์„œ $\nu_{1}$์„ ๊ณ ๋ คํ•˜๊ธฐ ์ด์ „์— ๊ฒฐ์ •๋˜๋Š” $f_{ce,s}$ ๊ฐ’์„ ๋‹ค์Œ์˜ ์‹ (7)๋กœ ํ‘œํ˜„๋˜๋Š” ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„๊ณ„์ˆ˜ $\nu_{2}$๋ฅผ ์œ ์ถœํ•˜์—ฌ $\nu_{2} f_{c k}$๋กœ ํ‘œํ˜„ํ•˜์˜€๋‹ค. ๋”ฐ๋ผ์„œ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ $f_{ce,s}$ ๋Š” $\nu_{1} \nu_{2} f_{c k}$๋กœ ๊ฒฐ์ •๋œ๋‹ค. ๋ช‡ ๊ฐ€์ง€ ์„ค๊ณ„๋ณ€์ˆ˜์˜ ์กฐํ•ฉ์— ๋Œ€ํ•ด ์ˆ˜์น˜ํ•ด์„์  ๊ธฐ๋ฒ•์œผ๋กœ ๊ฒฐ์ •ํ•œ $\nu_{2}$๊ฐ’์€ Fig. 3๊ณผ ๊ฐ™๋‹ค. ์ˆ˜์น˜ํ•ด์„๋ชจ๋ธ์˜ ์„ค๊ณ„๋ณ€์ˆ˜๋กœ ํœจ์ฒ ๊ทผ๋น„๋ฅผ ๊ณ ๋ คํ•˜์˜€์ง€๋งŒ Fig. 3์—์„œ ํ™•์ธํ•  ์ˆ˜ ์žˆ๋“ฏ์ด ํœจ์ฒ ๊ทผ๋น„๊ฐ€ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„์— ๋ฏธ์น˜๋Š” ์˜ํ–ฅ์ด ํฌ์ง€ ์•Š์•„ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ์‹์—์„œ ํœจ์ฒ ๊ทผ๋น„๋ฅผ ์ œ์™ธ์‹œ์ผฐ๋‹ค.

(7)
$\nu_{2}=-\alpha(c / d-\beta)^{2}+\gamma$

Fig. 3. Coefficient of effective strength of inclined three-dimensional concrete strut

../../Resources/kci/JKCI.2019.31.1.049/fig3.png

์—ฌ๊ธฐ์„œ, ๊ณ„์ˆ˜ $\alpha$, $\beta$, $\gamma$๋Š” ๋‹ค์Œ๊ณผ ๊ฐ™๋‹ค.

(8a)
ฮฑ   =   0 . 4   +   0 . 5   w / d ฮฒ   =   2 . 2   -   2   w / d ฮณ   =   2 . 5   -   2   w / d f o r   w / d โ‰ค 0 . 5          

(8b)
ฮฑ   = 0 . 6 ฮฒ   =   1 . 2   -   0 . 2   w / d ฮณ   =   1 . 5   -   0 . 1   w / d f o r   w / d > 0 . 5          

Fig. 3 ๋ฐ ์‹ (7)๋กœ๋ถ€ํ„ฐ, $c/d$๊ฐ€ 1์ด๋ฉฐ $w/d$๊ฐ€ 0.2 ๋ฐ 0.6์ธ ๊ฒฝ์šฐ $\nu_{2}$ ๊ฐ’์€ ๊ฐ๊ฐ 1.78 ๋ฐ 1.43์œผ๋กœ ์‚ฐ์ •๋˜๊ณ , $c/d$๊ฐ€ 0.5์ด๋ฉฐ $w/d$๊ฐ€ 0.2 ๋ฐ 0.6์ธ ๊ฒฝ์šฐ $\nu_{2}$ ๊ฐ’์€ ๊ฐ๊ฐ 1.26 ๋ฐ 1.23์ž„์„ ์•Œ ์ˆ˜ ์žˆ๋‹ค. ์ฆ‰ $w/d$๊ฐ€ ์ปค์งˆ์ˆ˜๋ก ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ๊ฐ’์ด ์ž‘์•„์ง€๋Š” ๊ฒฝํ–ฅ์„ ๋ณด์ธ๋‹ค. ์ด๋Š” $w/d$๊ฐ€ ์ปค์งˆ ๋•Œ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์ข…์ถ•์ด ์ˆ˜ํ‰๊ณผ ์ด๋ฃจ๋Š” ๊ฐ๋„๊ฐ€ ์ž‘์•„์ง€๋ฉฐ, ์ด๋กœ ์ธํ•ด ์ŠคํŠธ๋Ÿฟ์˜ ํšก์ถ• ๋ฐฉํ–ฅ์˜ ์ธ์žฅ์‘๋ ฅ์ด ๋” ์ปค์ง€๊ธฐ ๋•Œ๋ฌธ์ด๋‹ค. $w/d$๊ฐ€ 0.2์ด๋ฉฐ $c/d$๊ฐ€ 0.5, 1, 1.5, 2์ธ ๊ฒฝ์šฐ $\nu_{2}$ ๊ฐ’์€ ๊ฐ๊ฐ 1.26, 1.78, 2.06, 2.08๋กœ, $c/d$๊ฐ€ ์ปค์งˆ์ˆ˜๋ก ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ๊ฐ’์ด ์ปค์ง์„ ์•Œ ์ˆ˜ ์žˆ๋‹ค. $w/d$๊ฐ€ 0.4์ด๊ณ  $c/d$๊ฐ€ 0.5, 1, 1.5, 2์ธ ๊ฒฝ์šฐ ๊ฐ๊ฐ 1.21, 1.60, 1.69, 1.48๋กœ, $c/d$๊ฐ€ 1.5์ด์ƒ์ด ๋˜๋Š” ๊ฒฝ์šฐ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ๊ฐ’์ด ์ž‘์•„์ง์„ ์•Œ ์ˆ˜ ์žˆ๋‹ค. ์ด๋Š” ๋™์ผํ•œ $w/d$์—์„œ ๊ธฐ๋‘ฅ์˜ ํฌ๊ธฐ๊ฐ€ ์ปค์ง€๋ฉด ์ŠคํŠธ๋Ÿฟ์˜ ๊ฐ๋„๊ฐ€ ์ž‘์•„์ง€๊ธฐ ๋•Œ๋ฌธ์ด๋‹ค. $c/d$๊ฐ€ 1.0 ๊นŒ์ง€๋Š” $w/d$์™€ ๊ด€๊ณ„์—†์ด ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ๊ฐ’์ด ์ปค์ง€๋Š” ๊ฒƒ์„ ์•Œ ์ˆ˜ ์žˆ๋Š”๋ฐ, ์ด๋Š” ์ˆ˜์ง์˜ ๊ธฐ๋‘ฅ ํ•˜์ค‘์ด ๋” ๋„“๊ฒŒ ๋ถ„ํฌ๋˜๋ฉด์„œ ์••์ถ•์ฃผ์‘๋ ฅ ๋ฐฉํ–ฅ๊ณผ ์ŠคํŠธ๋Ÿฟ์˜ ์ข…์ถ• ์‚ฌ์ด์˜ ๊ฐ๋„ ์ฐจ์ด๊ฐ€ ์ค„์–ด๋“ค๊ธฐ ๋•Œ๋ฌธ์ธ ๊ฒƒ์œผ๋กœ ๋ถ„์„๋œ๋‹ค.

์‹ (7) ๋ฐ ์‹ (8)์€ ๋งค์šฐ ๋‹ค์–‘ํ•œ ์„ค๊ณ„๋ณ€์ˆ˜์˜ ์กฐํ•ฉ์— ๋Œ€ํ•ด ์ˆ˜์น˜ํ•ด์„์  ๊ธฐ๋ฒ•์œผ๋กœ ๊ฒฐ์ •ํ•œ $\nu_{2}$ ๊ฐ’์„ ๋‹ค์Œ์˜ 3๋‹จ๊ณ„ ๊ณผ์ •์„ ํ†ตํ•ด ์œ ์ถœํ•œ ๊ฒƒ์ด๋‹ค. ๋‹จ๊ณ„ 1: Fig. 3(d) ๋ฐ Fig. 4(a)์™€ ๊ฐ™์ด ํŒŒ์ผ์บก์˜ ์ฃผ์š” ๋ณ€์ˆ˜์ธ $w/d$ ๋ฐ $c/d$์™€ ์ˆ˜์น˜ํ•ด์„์  ๊ธฐ๋ฒ•์œผ๋กœ ๊ฒฐ์ •ํ•œ $\nu_{2}$ ๊ฐ’๊ณผ ๊ด€๊ณ„๋ฅผ ํŒŒ์•…ํ•œ๋‹ค. $\nu_{2}$ ๊ฐ’๊ณผ ๋‘ ๋ณ€์ˆ˜์™€์˜ ๊ด€๊ณ„ ์ค‘ ์ข€ ๋” ์ผ๊ด€๋œ ๊ด€๊ณ„๋ฅผ ๋ณด์ด๋Š” $c/d$๋ฅผ ๋ณ€์ˆ˜ ๊ฐ’์œผ๋กœ ๊ฒฐ์ •ํ•œ๋‹ค. ๋‹จ๊ณ„ 2: Fig. 4(a)์˜ ๊ทธ๋ž˜ํ”„๋ฅผ ๋ฌ˜์‚ฌํ•  ์ˆ˜ ์žˆ๋Š” ์‹์˜ ๊ธฐ๋ณธ ํ˜•ํƒœ๋ฅผ ์„ ์ •ํ•œ๋‹ค. ์ด ์—ฐ๊ตฌ์—์„œ๋Š” ๊ฐ€๋กœ์ถ• ๋ณ€์ˆ˜ $c/d$์— ๋Œ€ํ•œ 2์ฐจ์‹ ์ฆ‰ $\nu_{2}=-\alpha(c / d-\beta)^{2}+\gamma$๋ฅผ ๊ธฐ๋ณธ ์‹์œผ๋กœ ์„ ์ •ํ•˜์˜€๋‹ค. ๋‹จ๊ณ„ 3: ๊ธฐ๋ณธ ์‹์˜ ๊ณ„์ˆ˜ ๊ฐ’ $\alpha$, $\beta$, $\gamma$๋ฅผ ๊ณก์„ ์กฐ์ •์„ ํ†ตํ•ด ๊ฒฐ์ •ํ•œ๋‹ค. ๊ณก์„  ์กฐ์ •์€ ์—‘์…€ํ”„๋กœ๊ทธ๋žจ์„ ์ด์šฉํ•˜์—ฌ Fig. 4(b)์˜ ์˜ˆ์™€ ๊ฐ™์ด ๊ฐ ๊ทธ๋ž˜ํ”„์˜ ์ถ”์„ธ์„ ์„ ํ™•์ธํ•œ ํ›„, $w/d$์˜ ๋ณ€ํ™”์— ๋”ฐ๋ฅธ ๊ฐ ๊ณ„์ˆ˜๊ฐ’ $\alpha$, $\beta$, $\gamma$๋ฅผ ์‹ (8)๊ณผ ๊ฐ™์€ ์ˆ˜์‹์œผ๋กœ ํ‘œํ˜„ํ•œ๋‹ค. Fig. 4(c)๋Š” ์ˆ˜์น˜ํ•ด์„์  ๊ธฐ๋ฒ•์œผ๋กœ ๊ฒฐ์ •ํ•œ $w / d=0.6$์ผ ๋•Œ์˜ $\nu_{2}$ ๊ฐ’๊ณผ ์‹ (7) ๋ฐ ์‹ (8)์— ์˜ํ•ด ๊ฒฐ์ •ํ•œ $\nu_{2}$ ๊ฐ’์„ ๋น„๊ตํ•œ ๊ฒƒ์ด๋‹ค.

Fig. 4. Graphs for extracting equation of effective strut strength

../../Resources/kci/JKCI.2019.31.1.049/fig4.png

4. ํƒ€๋‹น์„ฑ ๊ฒ€์ฆ

์ด ์—ฐ๊ตฌ์—์„œ ์ œ์•ˆํ•œ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ ์œ ํšจ๊ฐ•๋„ ์‹์˜ ํƒ€๋‹น์„ฑ์„ ๊ฒ€์ฆํ•˜๊ธฐ ์œ„ํ•˜์—ฌ ํŒŒ๊ดด์‹คํ—˜์ด ์ˆ˜ํ–‰๋œ Clarke(1973)[10]์˜ 13๊ฐœ, Sabnis and Gogate(1984)[22]์˜ 8๊ฐœ, ๊ทธ๋ฆฌ๊ณ  Suzuki et al.(1998[25], 1999[26], 2000[27], 2002[24])์˜ 94๊ฐœ ๋“ฑ ์ด 115๊ฐœ์˜ ์ฒ ๊ทผ์ฝ˜ํฌ๋ฆฌํŠธ ํŒŒ์ผ์บก์˜ ํŒŒ๊ดด๊ฐ•๋„๋ฅผ Fig. 1(b)์˜ 8์ ˆ์  3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ์„ ์ด์šฉํ•˜์—ฌ ์˜ˆ์ธกํ•˜์˜€๋‹ค. ํŒŒ์ผ์บก ์‹œํ—˜์ฒด์˜ ์ œ์›์€ Table 1๊ณผ ๊ฐ™์œผ๋ฉฐ, ๊ฐ ์‹œํ—˜์ฒด์˜ ํ˜•์ƒ ๋ฐ ๋ฐฐ๊ทผ์ƒ์„ธ๋Š” ์ฐธ๊ณ ๋ฌธํ—Œ์— ์†Œ๊ฐœ๋˜์–ด ์žˆ๋‹ค.

Table 1. Specifications of four-pile caps tested to failure

Researcher

No. of Pile Caps

$w/d$

$d$ (mm)

Col. Size (mm)

Pile Size (mm)

$f_ {cu}$ (MPa)

$f_ {y}$ (MPa)

$\rho$ (%)

Re-bar Layout

Clarke (1973)[10]

13

0.25-0.49

400

200, S

200, R

18.0-35.0

510

0.141-0.235

B & G

Sabnis & Gogate (1984)[22]

8

0.54-0.58

109-117

76, R

76, R

17.9-41.0

434-886

0.136-1.287

G

Suzuki et al. (1998)[25]

28

0.40-0.80

150-250

250-300, S

150, R

18.9-31.3

345-413

0.228-0.564

B & G

Suzuki et al. (1999)[26]

18

0.33-0.58

250-300

250, S

150, R

25.6-30.9

356-383

0.106-0.317

G

Suzuki et al. (2000)[27]

30

0.29-0.67

150-350

200-300, S

150, R

24.5-29.4

358-383

0.181-0.272

G

Suzuki et al. (2002)[24]

18

0.33-0.50

300

200-300, S

150, R

20.2-37.9

353

0.267

G

Total

115

0.29-0.80

109-400

76-300

76-200, R

17.9-41.0

345-886

0.106-1.287

B, G

$w$: distance from the face of column to the center of the nearest pile; $d$: effective depth; R, S, B, G: round, square, bunched, grid

์ฒ ๊ทผ์ฝ˜ํฌ๋ฆฌํŠธ ํŒŒ์ผ์บก์˜ ํŒŒ๊ดด๊ฐ•๋„ ์˜ˆ์ธก๊ณผ์ •์€ Sabnis and Gogate(1984)[22]์˜ ํŒŒ์ผ์บก ์‹œํ—˜์ฒด ์ค‘ Fig. 5์˜ ๊ธฐํ•˜ํ•™์  ํ˜•์ƒ ๋ฐ ๋ฐฐ๊ทผ์ƒ์„ธ๋ฅผ ๊ฐ–๋Š” SS5๋ฅผ ์˜ˆ๋กœ ๋“ค์–ด ์†Œ๊ฐœํ•˜์˜€๋‹ค. ์‹œํ—˜์ฒด SS5์˜ ์œ ํšจ๊นŠ์ด์— ๋Œ€ํ•œ ๊ธฐ๋‘ฅ๋ฉด์—์„œ ๊ฐ€์žฅ ๊ฐ€๊นŒ์šด ํŒŒ์ผ ์ค‘์‹ฌ๊นŒ์ง€์˜ ๊ฑฐ๋ฆฌ์˜ ๋น„, ์ฆ‰ ์ „๋‹จ๊ฒฝ๊ฐ„๋น„ $w/d$๋Š” 0.58์ด๋‹ค. ์ด ์‹œํ—˜์ฒด์˜ ํŒŒ๊ดด๊ฐ•๋„ ์˜ˆ์ธก์„ ์œ„ํ•˜์—ฌ Fig. 6์˜ 8์ ˆ์  3์ฐจ์› ๋ถ€์ •์ • ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ์„ ์ด์šฉํ•˜์˜€๋‹ค. ์ด ๋ชจ๋ธ์˜ ์ฒ ๊ทผ ํƒ€์ด๋Š” ์‹œํ—˜์ฒด ํ•˜๋‹จ๋ถ€์— ๋ฐฐ์น˜๋œ ์ธ์žฅ์ฒ ๊ทผ์˜ ๋„์‹ฌ์— ์œ„์น˜์‹œ์ผฐ์œผ๋ฉฐ, ์ƒ๋‹จ๋ถ€์˜ ์ˆ˜ํ‰ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์ค‘์‹ฌ์„ ์€ ํ•˜๋‹จ๋ถ€ ์ฒ ๊ทผ ํƒ€์ด์˜ ์ค‘์‹ฌ์„ ์—์„œ 0.9$d$๋–จ์–ด์ง„ ๊ณณ์— ์œ„์น˜์‹œ์ผฐ๋‹ค. ํŒŒ์ผ์บก ์‹œํ—˜์ฒด์˜ ํŒŒ๊ดด๊ฐ•๋„๋Š” ์ŠคํŠธ๋Ÿฟ, ํƒ€์ด, ๊ทธ๋ฆฌ๊ณ  ์ ˆ์ ์˜์—ญ ๋“ฑ์˜ ํ•˜์ค‘์ „๋‹ฌ๋Šฅ๋ ฅ์„ ๊ฒ€ํ† ํ•˜๋Š”, ์ฆ‰ ํ•„์š”๋‹จ๋ฉด์ ๊ณผ ์ตœ๋Œ€๋‹จ๋ฉด์ ์˜ ๋น„๋ฅผ ๋น„๊ตํ•˜๋Š” ACI 445(2002[1], 2010[2])์˜ ๋ฐฉ๋ฒ•์œผ๋กœ ๊ตฌํ•˜์˜€๋‹ค. ACI 445์˜ ๋ฐฉ๋ฒ•์„ ์ ์šฉํ•˜๊ธฐ ์œ„ํ•ด์„œ๋Š” ์ŠคํŠธ๋Ÿฟ, ํƒ€์ด, ๊ทธ๋ฆฌ๊ณ  ์ ˆ์ ์˜์—ญ์˜ ์ตœ๋Œ€๋‹จ๋ฉด์ ์„ ์ •์˜ํ•ด์•ผ ํ•˜๋ฉฐ, ๋˜ํ•œ ์ด๋“ค ์š”์†Œ์˜ ์œ ํšจ๊ฐ•๋„๋ฅผ ๊ฒฐ์ •ํ•ด์•ผ ํ•œ๋‹ค. ์ŠคํŠธ๋Ÿฟ์˜ ์ตœ๋Œ€๋‹จ๋ฉด์  ๋ฐ ์••์ถ• ๋ฐ ์ธ์žฅ ์š”์†Œ์™€ ์ ‘ํ•˜๋Š” ์ ˆ์ ์˜์—ญ ์ˆ˜์ง๊ฒฝ๊ณ„๋ฉด์˜ ์ตœ๋Œ€๋‹จ๋ฉด์ ์€ ACI 445(2002)[1]์˜ ๋ฐฉ๋ฒ•์ธ ํ•˜์ค‘ํŒ ๋ฐ ์ง€์ง€ํŒ์˜ ํฌ๊ธฐ์™€ ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ์˜ ํ˜•์ƒ์„ ๊ณ ๋ คํ•˜์—ฌ Fig. 7๊ณผ ๊ฐ™์ด ๊ฒฐ์ •ํ•˜์˜€๋‹ค. ์ฒ ๊ทผ ํƒ€์ด์˜ ์ตœ๋Œ€๋‹จ๋ฉด์ ์€ ์ฒ ๊ทผ ํƒ€์ด์˜ ์œ„์น˜์— ๋ฐฐ์น˜๋œ ํœจ์ฒ ๊ทผ๋Ÿ‰์œผ๋กœ ์ทจํ•˜์˜€๋‹ค. ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„๋Š” 2์žฅ์— ์†Œ๊ฐœํ•œ ์„ค๊ณ„๊ธฐ์ค€๊ณผ 3์žฅ์˜ ์ œ์•ˆ์‹ (7)์„ ์ด์šฉํ•˜์—ฌ ๊ตฌํ–ˆ์œผ๋ฉฐ, ์ฝ˜ํฌ๋ฆฌํŠธ ํƒ€์ด์˜ ์œ ํšจ๊ฐ•๋„๋กœ๋Š” ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์ธ์žฅ๊ฐ•๋„ 0.62$\sqrt{f_{d k}}(\mathrm{MPa})$๋ฅผ ์ทจํ•˜์˜€๋‹ค. ์ฒ ๊ทผ ํƒ€์ด์˜ ์œ ํšจ๊ฐ•๋„๋กœ๋Š” ์ฒ ๊ทผ์˜ ํ•ญ๋ณต๊ฐ•๋„ $f_ {y}$๋ฅผ ์ทจํ•˜์˜€๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„๊ฐ€ ํŒŒ์ผ์บก์˜ ๊ทนํ•œ๊ฐ•๋„์— ๋ฏธ์น˜๋Š” ์˜ํ–ฅ์˜ ๋ถ„์„์„ ํ†ตํ•ด 2์žฅ์—์„œ ์†Œ๊ฐœํ•œ ๊ฐ ๋ฐฉ๋ฒ• ๋ฐ ์ด ์—ฐ๊ตฌ์˜ ์ œ์•ˆ์‹ (7)์˜ ์ ํ•ฉ์„ฑ์„ ๊ฒ€์ฆํ•˜๊ธฐ ์œ„ํ•œ ๊ฒƒ์ด๋ฏ€๋กœ, ํŒŒ์ผ๊ณผ ์ŠคํŠธ๋Ÿฟ์ด ๋งŒ๋‚˜๋Š” CTT ์ ˆ์ ์˜์—ญ ๋ฐ ๊ธฐ๋‘ฅ๊ณผ ์ŠคํŠธ๋Ÿฟ์ด ๋งŒ๋‚˜๋Š” CCC ์ ˆ์ ์˜์—ญ์˜ ์œ ํšจ๊ฐ•๋„ $f_ {ce,n}$์€ ๊ณตํ†ต์ ์œผ๋กœ Bergmeister et al.(1993)[7]์ด ์ œ์•ˆํ•œ 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ์˜ ์ ˆ์ ์˜์—ญ ๊ฐ•๋„์‹์ธ ์‹ (9)๋กœ๋ถ€ํ„ฐ ๊ฒฐ์ •ํ•˜์˜€๋‹ค.

Fig. 5. Reinforcement details and geometry of four-pile cap SS5

../../Resources/kci/JKCI.2019.31.1.049/fig5.png

Fig. 6. Three-dimensional strut-and-tie model for four-pile cap SS5

../../Resources/kci/JKCI.2019.31.1.049/fig6.png

Fig. 7. Maximum available cross-sectional areas of struts, ties, and nodes

../../Resources/kci/JKCI.2019.31.1.049/fig7.png

(9)
$f_{ce, n}=\nu_{e}\left(A_{2} / A_{1}\right)^{0.5} f_{c k}$

์—ฌ๊ธฐ์„œ, $A_ {1}$๋Š” ์ง€์ง€ํŒ(ํ•˜์ค‘ํŒ)์˜ ๋ฉด์ ์ด๋ฉฐ, $A_ {2}$๋Š” $A_ {1}$์„ 1 ๋Œ€ 2์˜ ์ˆ˜์ง ๋Œ€ ์ˆ˜ํ‰ ๋น„๋กœ ํ™•๋Œ€ํ–ˆ์„ ๋•Œ์˜ ์ตœ๋Œ€๋ฉด์ ์ด๋ฉฐ, $\nu_{e}\left(A_{2} / A_{1}\right)^{0.5}$ ๋ฐ $\sqrt{A_{2} / A_{1}}$์˜ ์ตœ๋Œ€๊ฐ’์€ 2.5 ๋ฐ 2.0์ด๋‹ค. ๋˜ํ•œ $\nu_{e}$๋Š” ๋‹ค์Œ๊ณผ ๊ฐ™๋‹ค.

(10)
$\nu_{e}=\left\{\begin{array}{ll}{0.80} & { for \quad f_{c k} \leq 28} \\ {0.90-0.25 f_{c k} / 70} & { for \quad 28 < f_{c k} < 70} \\ {0.65} & { for \quad f_{ck} \geq 70}\end{array}\right.$

์œ„ ์‹์—์„œ $f_ {ck}$์˜ ๋‹จ์œ„๋Š” MPa์ด๋‹ค.

Table 2๋Š” ์ƒ๋‹จ๋ถ€์˜ ์ˆ˜ํ‰ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์ค‘์‹ฌ์„ ์ด ํ•˜๋‹จ๋ถ€ ์ฒ ๊ทผ ํƒ€์ด์˜ ์ค‘์‹ฌ์„ ์—์„œ 0.9$d$๋งŒํผ ๋–จ์–ด์ง„ ๊ณณ์— ์œ„์น˜ํ•œ Fig. 6์˜ 3์ฐจ์› ๋ถ€์ •์ • ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ, ACI 445์˜ ์ ˆ์ ์˜์—ญ ํ˜•์ƒ๊ฒฐ์ • ๋ฐฉ๋ฒ•, Bergmeister et al.(1993)[7]์˜ ์ ˆ์ ์˜์—ญ ์œ ํšจ๊ฐ•๋„, ๊ทธ๋ฆฌ๊ณ  ์ œ์•ˆ์‹ (7)๋กœ๋ถ€ํ„ฐ ๊ตฌํ•œ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ๋“ฑ์„ ์ด์šฉํ•˜์—ฌ ํŒŒ์ผ์บก ์‹œํ—˜์ฒด SS5์˜ ํŒŒ๊ดด๊ฐ•๋„ ์˜ˆ์ธก๊ณผ์ •์„ ๋ณด์ธ ๊ฒƒ์ด๋‹ค. ์‹œํ—˜์ฒด SS5์˜ ์ „๋‹จ๊ฒฝ๊ฐ„๋น„ $w/d$๊ฐ€ 0.58์ด๋ฏ€๋กœ, ์‹ (8b)๋กœ๋ถ€ํ„ฐ $\alpha$, $\beta$, $\gamma$๋Š” ๊ฐ๊ฐ 0.60, 1.084, 1.442๋กœ, ๊ทธ๋ฆฌ๊ณ  ์‹ (7)๋กœ๋ถ€ํ„ฐ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„๊ณ„์ˆ˜ $\nu_{2}$๋Š” 1.353์œผ๋กœ ๊ฒฐ์ •๋œ๋‹ค. ๋”ฐ๋ผ์„œ Table 2์„œ, ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„๊ณ„์ˆ˜ $\nu_{s}$(=1.291)๋Š” ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์••์ถ•๊ฐ•๋„์˜ ์˜ํ–ฅ์„ ๊ณ ๋ คํ•˜๋Š” ๊ณ„์ˆ˜ $\nu_{1}$(=1.1-0.25$f_ {ck}$/70=0.954)๊ณผ $\nu_{2}$(=1.353)๋ฅผ ๊ณฑํ•˜์—ฌ ๊ตฌํ•˜์˜€๋‹ค.

Table 2. Prediction of ultimate strength of four-pile cap SS5 based on effective strut strength equation of present study (a) Examination of failure strengths of struts and ties at the first failure

Element No.

Element Type

$\nu_{s}$

$f_ {ck}$ (MPa)

$f_ {ce,s}$ (=$\nu_{s} f_ {ck}$, MPa)

$F_ {u}$ (kN)

$A_ {req.}$ (=$F_ {u} / f_ {ce,s}$ , mm2)

$A_ {prov.}$ (mm2)

$\frac{A_{prov.}}{A_{req.}}$

Fail/Safe

S1

Strut

1.291

41.0

52.9

102.6

1939.3

1633

0.842

X(Fail)

Element No.

Element Type

$\nu_{t}$

$f_ {y}$ (MPa)

$f_ {ce,t}$ (=$\nu_{t} f_ {y}$, MPa)

$F_ {u}$ (kN)

$A_ {req.}$ (=$F_ {u} / f_ {ce,t}$ , mm2)

$A_ {prov.}$ (mm2)

$\frac{A_{prov.}}{A_{req.}}$

Safety

T1

Tie

1.000

498.0

498.0

32.5

65

96

1.473

โ—‹(Safe)

T2

C. Tie

-

41.0

3.96

32.5

8215

6614

0.805

X

$\nu_{s}$: coeff. of eff. strength of strut (=$\nu_{1} \nu_{2}$); $\nu_{t}$: coeff. of eff. strength of tie; $f_{cu}$ values in Table 1 were regarded as $f_{ck}$ in strut-and-tie model analysis; $f_{ce,s}$ and $f_{ce,t}$ : eff. strength of strut and tie

Table 2. (b) Examination of failure strengths of struts and ties at the second failure

Element No.

Element Type

$\nu_{s}$

$f_ {ck}$ (MPa)

$f_ {ce,s}$ (=$\nu_{s} f_ {ck}$, MPa)

$F_ {u}$ (kN)

$A_ {req.}$ (=$F_ {u} / f_ {ce,s}$ , mm2)

$A_ {prov.}$ (mm2)

$\frac{A_{prov.}}{A_{req.}}$

Fail/Safe

S1

Strut

1.291

41.0

52.9

102.6

1939.3

71.1

0.037

X

Element No.

Element Type

$\nu_{t}$

$f_ {y}$ (MPa)

$f_ {ce,t}$ (=$\nu_{t} f_ {y}$, MPa)

$F_ {u}$ (kN)

$A_ {req.}$ (=$F_ {u} / f_ {ce,t}$ , mm2)

$A_ {prov.}$ (mm2)

$\frac{A_{prov.}}{A_{req.}}$

Fail/Safe

T1

Tie

1.000

498.0

498.0

55.5

111.5

43.7

0.391

X

Table 2. (c) Examination of failure strengths of nodal zones

Node No.

Node Type

$\nu_{n}$

$f_{ck}$ (MPa)

$f_{ce,n}$ (=$\nu_{n} f_{ck}$, MPa)

$F_{u}$ (kN)

$A_{req.}$ (=$F_{u} / f_{ce,n}$, mm2)

$A_{prov.}$ (mm2)

$\frac{A_{prov.}}{A_{req.}}$

Fail/Safe

1

CCC

1.507

41.0

61.79

V

55.6

899

1140

1.27

โ—‹

S1

86.4

1397

1633

1.17

โ—‹

2

CTT

1.254

41.0

51.42

R

55.6

1081

4560

4.22

โ—‹

S1

86.4

1680

7998

4.76

โ—‹

T1

28.2

549

6614

12.05

โ—‹

T2

26.2

509

6614

12.98

โ—‹

$\nu_{n}$: coeff. of eff. strength of nodal zone(=$\nu_{e} \sqrt{A_{2} / A_{1}}$); $\nu_{e}$, $A_{1}$, $A_{2}$: refer to Eqn. (10); $f_{ce,n}$: eff. strength of nodal zone

ํŒŒ๊ดด๊ฐ•๋„๋ฅผ ์˜ˆ์ธกํ•œ ๊ฒฐ๊ณผ, 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ์˜ 1์ฐจ ํŒŒ๊ดด๋Š” Table 2(a)์— ๋‚˜ํƒ€๋‚œ ๊ฒƒ๊ณผ ๊ฐ™์ด ์ฝ˜ํฌ๋ฆฌํŠธ ํƒ€์ด T2๊ฐ€ ์ตœ๋Œ€๋กœ ๋ฐ›์„ ์ˆ˜ ์žˆ๋Š” ํ•˜์ค‘์ƒํƒœ, ์ฆ‰ ์‹คํ—˜ํŒŒ๊ดดํ•˜์ค‘์˜ 80.5%์ธ 212.5 kN์—์„œ ๋ฐœ์ƒํ•˜์˜€๋‹ค. 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ์€ 1์ฐจ ๋ถ€์ •์ • ํŠธ๋Ÿฌ์Šค ๊ตฌ์กฐ์ด๋ฏ€๋กœ ์ด ๋ชจ๋ธ์€ 1์ฐจ ํŒŒ๊ดด ํ›„์—๋„ ์ถ”๊ฐ€์ ์ธ ํ•˜์ค‘์„ ๋ฐ›์„ ์ˆ˜ ์žˆ๋‹ค. ์ถ”๊ฐ€์ ์ธ ํ•˜์ค‘์„ ์ž‘์šฉ์‹œํ‚จ ๊ฒฐ๊ณผ, 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ์˜ 2์ฐจ ํŒŒ๊ดด๋Š” Table 2(b)์— ๋‚˜ํƒ€๋‚œ ๊ฒƒ๊ณผ ๊ฐ™์ด ์ŠคํŠธ๋Ÿฟ S1์˜ ํŒŒ๊ดด์— ์˜ํ•ด ์‹คํ—˜ํŒŒ๊ดดํ•˜์ค‘์˜ 3.7%์ธ 9.8 kN์—์„œ ๋ฐœ์ƒํ•˜์˜€๋‹ค. 2์ฐจ ํŒŒ๊ดด ํ›„ 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ์€ ๋ถˆ์•ˆ์ „ ํŠธ๋Ÿฌ์Šค ๊ตฌ์กฐ๊ฐ€ ๋˜์–ด ์ถ”๊ฐ€์ ์ธ ํ•˜์ค‘์„ ์ง€์ ์œผ๋กœ ์ „๋‹ฌํ•  ์ˆ˜ ์—†๋‹ค. ์ŠคํŠธ๋Ÿฟ๊ณผ ํƒ€์ด ์š”์†Œ์˜ ๊ฐ•๋„๋ฅผ ๊ฒ€ํ† ํ•œ ํ›„ 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ์ด ๋ฐ›์„ ์ˆ˜ ์žˆ๋Š” ์ตœ๋Œ€ํ•˜์ค‘ 222.3 kN(=212.5+9.8) ํ•˜์—์„œ Table 2(c)์™€ ๊ฐ™์ด ์ ˆ์ ์˜์—ญ์˜ ๊ฐ•๋„๋ฅผ ๊ฒ€ํ† ํ•˜์˜€๋‹ค. ์ ˆ์ ์˜์—ญ ๊ฐ•๋„๊ฒ€ํ†  ๊ฒฐ๊ณผ, ํŒŒ์ผ์บก ์ƒ๋‹จ์˜ CCC ๋ฐ ํ•˜๋‹จ์˜ CCT ์ ˆ์ ์˜์—ญ์€ ์ŠคํŠธ๋Ÿฟ๊ณผ ํƒ€์ด์˜ ๋‹จ๋ฉด๋ ฅ์„ ํŒŒ์ผ๋กœ ์ „๋‹ฌํ•จ์— ์ถฉ๋ถ„ํ•˜์˜€๋‹ค. ๋”ฐ๋ผ์„œ ํ˜„ ์—ฐ๊ตฌ์˜ ์ ˆ์ ์˜์—ญ ์œ ํšจ๊ฐ•๋„ ๊ฒฐ์ •๋ฐฉ๋ฒ•์„ ์ด์šฉํ•˜์—ฌ ์˜ˆ์ธกํ•œ ํŒŒ์ผ์บก ์‹œํ—˜์ฒด SS5์˜ ํŒŒ๊ดด๊ฐ•๋„๋Š” ์ŠคํŠธ๋Ÿฟ๊ณผ ํƒ€์ด์˜ ํ•˜์ค‘์ „๋‹ฌ์„ฑ๋Šฅ์— ์˜ํ•ด ์‹คํ—˜ํŒŒ๊ดดํ•˜์ค‘์˜ 84.2 %์ธ 222.3 kN์œผ๋กœ ๊ฒฐ์ •๋˜์—ˆ๋‹ค. ์ด์™€ ๋™์ผํ•œ ์ ˆ์ฐจ์— ๋”ฐ๋ผ 115๊ฐœ ์‹œํ—˜์ฒด์˜ ํŒŒ๊ดด๊ฐ•๋„๋ฅผ ์˜ˆ์ธกํ•˜์˜€๋‹ค. ๋˜ํ•œ ๋ณธ ์—ฐ๊ตฌ์—์„œ ์ œ์•ˆํ•œ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ ์œ ํšจ๊ฐ•๋„ ์‹์˜ ์ ํ•ฉ์„ฑ์„ ๊ฒ€์ฆํ•˜๊ธฐ ์œ„ํ•ด EC2, FIB, ACI 318, AASHTO ๋“ฑ์˜ ์ŠคํŠธ๋Ÿฟ ์œ ํšจ๊ฐ•๋„ ์‹์„ ์ด์šฉํ•˜์—ฌ ํŒŒ๊ดด์‹คํ—˜์ด ์ˆ˜ํ–‰๋œ 115๊ฐœ ํŒŒ์ผ๊ฐ•๋„๋ฅผ ์˜ˆ์ธกํ•˜์˜€๋‹ค. ๋˜ํ•œ ๋ณธ ์—ฐ๊ตฌ์—์„œ ์ œ์•ˆํ•œ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ ์œ ํšจ๊ฐ•๋„ ์‹์˜ ์ ํ•ฉ์„ฑ์„ ๊ฒ€์ฆํ•˜๊ธฐ ์œ„ํ•ด EC2, FIB, ACI 318, AASHTO ๋“ฑ์˜ ์ŠคํŠธ๋Ÿฟ ์œ ํšจ๊ฐ•๋„ ์‹์„ ์ด์šฉํ•˜์—ฌ ํŒŒ๊ดด์‹คํ—˜์ด ์ˆ˜ํ–‰๋œ 115๊ฐœ ํŒŒ์ผ์บก์˜ ํŒŒ๊ดด๊ฐ•๋„๋ฅผ ์˜ˆ์ธกํ•˜์˜€๋‹ค. ์˜ˆ์ธกํ•œ ๊ฒฐ๊ณผ๋Š” Table 3 ๋ฐ Fig. 8๊ณผ ๊ฐ™๋‹ค.

Table 3. Ultimate strengths of four-pile caps predicted based on existing and proposed effective strut strength equations

Specimens

$P_ {test} / P_ {predicted}$

EC2 (2004)[12]

FIB (2010)[11]

ACI 318 (2014)[5]

AASHTO (2018)[4]

Present Study

Clarke (1973)[10]

Mean

2.64

3.07

2.80

2.48

1.36

STDEV

0.511

0.627

0.586

0.751

0.178

Sabnis & Gogate (1984)[22]

Mean

3.46

4.03

3.59

2.67

1.41

STDEV

0.298

0.379

0.445

0.374

0.200

Suzuki et al. (1998)[25]

Mean

1.37

1.50

1.41

1.25

1.24

STDEV

0.182

0.275

0.229

0.097

0.094

Suzuki et al. (1999)[26]

Mean

1.23

1.31

1.26

1.16

1.14

STDEV

0.301

0.400

0.333

0.179

0.169

Suzuki et al. (2000)[27]

Mean

1.19

1.27

1.21

1.13

1.09

STDEV

0.090

0.166

0.117

0.108

0.087

Suzuki et al. (2002)[24]

Mean

1.36

1.54

1.43

1.17

1.07

STDEV

0.368

0.475

0.420

0.214

0.083

Total (115*)

Mean

1.59

1.77

1.65

1.43

1.19

STDEV

0.729

0.899

0.786

0.611

0.167

COV(%)

45.9

50.8

47.7

42.7

14.1

*: Number of specimens; STDEV: Standard deviation; COV: Coefficient of variation; In all cases, the eff. strengths of nodal zones were determined from Eq. (9).

Fig. 8. Ultimate strengths of four-pile caps

../../Resources/kci/JKCI.2019.31.1.049/fig8.png

Table 3 ๋ฐ Fig. 8์—์„œ ์•Œ ์ˆ˜ ์žˆ๋“ฏ์ด, ํŒŒ์ผ์บก์˜ ํŒŒ๊ดด๊ฐ•๋„๋Š” ํ˜„ํ–‰ ์„ค๊ณ„๊ธฐ์ค€์˜ ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ์‹์„ ์‚ฌ์šฉํ•  ๊ฒฝ์šฐ ๋ชจ๋‘ ์ง€๋‚˜์น˜๊ฒŒ ๋ณด์ˆ˜์ ์œผ๋กœ ์˜ˆ์ธก๋˜์—ˆ๋‹ค. ๋ฐ˜๋ฉด์— ์ด ์—ฐ๊ตฌ์˜ ์ŠคํŠธ๋Ÿฟ ์œ ํšจ๊ฐ•๋„ ์‹์— ์˜ํ•ด์„œ๋Š” ํŒŒ์ผ์บก์˜ ํŒŒ๊ดด๊ฐ•๋„๊ฐ€ ํ‰๊ท ์ ์œผ๋กœ ๋งค์šฐ ์–‘ํ˜ธํ•˜๊ฒŒ ์˜ˆ์ธก๋˜์—ˆ๋‹ค. ์ด๋Ÿฌํ•œ ๊ฒฐ๊ณผ๋Š” ํ˜„ ์—ฐ๊ตฌ์˜ ์ŠคํŠธ๋Ÿฟ ์œ ํšจ๊ฐ•๋„ ์‹์ด ํŒŒ์ผ์บก๊ณผ ๊ฐ™์€ 3์ฐจ์› ๊ฑฐ๋™์ด ์ง€๋ฐฐ์ ์ธ ๊ตฌ์กฐ๋ถ€์žฌ์˜ ๊ฑฐ๋™์— ์˜ํ–ฅ์„ ๋ฏธ์น˜๋Š” ์—ฌ๋Ÿฌ ์š”์ธ๋“ค์„ ์ž˜ ๋ฐ˜์˜ํ•˜๊ธฐ ๋•Œ๋ฌธ์ธ ๊ฒƒ์œผ๋กœ ํŒ๋‹จ๋œ๋‹ค. Table 4๋Š” ์ฝ˜ํฌ๋ฆฌํŠธ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ๊ฐ’์— ๋”ฐ๋ฅธ ํŒŒ์ผ์บก์˜ ํŒŒ๊ดด๊ฐ•๋„ ์˜ˆ์ธก๊ฒฐ๊ณผ๋ฅผ ์ „๋‹จ๊ฒฝ๊ฐ„๋น„($w/d$), ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์••์ถ•๊ฐ•๋„, ๊ทธ๋ฆฌ๊ณ  ํœจ ์ฒ ๊ทผ๋น„์— ๋”ฐ๋ผ ๋ถ„๋ฅ˜ํ•˜์—ฌ ๋น„๊ตํ•œ ๊ฒƒ์œผ๋กœ, ์ด ์—ฐ๊ตฌ์˜ ์ŠคํŠธ๋Ÿฟ ์œ ํšจ๊ฐ•๋„ ์‹์€ ํŒŒ์ผ์บก์˜ ๊ฑฐ๋™์— ์ง€๋ฐฐ์ ์ธ ์˜ํ–ฅ์„ ๋ฏธ์น˜๋Š” ์ด๋“ค ์„ค๊ณ„๋ณ€์ˆ˜์˜ ๋ชจ๋“  ๋ฒ”์œ„์—์„œ ์ •ํ™•ํ•˜๊ณ  ์ผ๊ด€๋˜๊ฒŒ ์ ์šฉ๋  ์ˆ˜ ์žˆ์Œ์„ ์•Œ ์ˆ˜ ์žˆ๋‹ค.

Table 4. Classification of predicted ultimate strengths according to primary design variables

Design variables

$P_ {test} / P_ {predicted}$

EC2 (2004)[12]

FIB (2010)[11]

ACI 318 (2014)[5]

AASHTO (2018)[4]

Present Study

$w / d < 0.5$ (53*)

Mean

1.56

1.73

1.62

1.49

1.19

STDEV

0.679

0.841

0.748

0.681

0.153

$w / d \geq 0.5$ (62*)

Mean

1.61

1.81

1.67

1.38

1.18

STDEV

0.774

0.951

0.822

0.543

0.179

$f_{c u} < 27 \mathrm{MPa}$ (57*)

Mean

1.68

1.92

1.77

1.49

1.17

STDEV

0.761

0.935

0.843

0.712

0.179

$f_{c u} \geq 27 \mathrm{MPa}$ (58*)

Mean

1.50

1.63

1.52

1.37

1.20

STDEV

0.691

0.846

0.711

0.491

0.154

$\rho < 0.25 \% $ (60*)

Mean

1.61

1.78

1.66

1.51

1.18

STDEV

0.788

0.965

0.852

0.731

0.179

$\rho \geq 0.25 \% $ (55*)

Mean

1.57

1.77

1.63

1.34

1.19

STDEV

0.665

0.830

0.715

0.432

0.155

*: Number of specimens

5. ๊ฒฐ ๋ก 

ํ˜„ํ–‰ ์„ค๊ณ„๊ธฐ์ค€์˜ ์ŠคํŠธ๋Ÿฟ ์œ ํšจ๊ฐ•๋„ ์‹๋“ค์€ 2์ฐจ์› ์„ค๊ณ„์˜์—ญ์˜ ์‹คํ—˜ ๋ฐ ํ•ด์„์— ๊ทผ๊ฑฐํ•œ ๋ช‡๋ช‡์˜ ํŠน์ •ํ•œ ๊ฐ’์œผ๋กœ ํ‘œํ˜„๋˜๋ฏ€๋กœ ์ด๋ฅผ 3์ฐจ์› ๊ฑฐ๋™์ด ์ง€๋ฐฐ์ ์ธ ํŒŒ์ผ์บก์˜ ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ์„ค๊ณ„์— ์ ์šฉํ•˜๋Š” ๊ฒƒ์€ ์ ์ ˆํ•˜์ง€ ์•Š๋‹ค. ์ด๋Ÿฌํ•œ ๋ฌธ์ œ๋ฅผ ํ•ด๊ฒฐํ•˜๊ธฐ ์œ„ํ•˜์—ฌ ์ˆ˜์น˜ํ•ด์„์  ๊ธฐ๋ฒ•์— ๊ทผ๊ฑฐํ•œ 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ๊ฒฐ์ •๋ฐฉ๋ฒ•์ด ์ตœ๊ทผ์— ์ œ์•ˆ๋˜์—ˆ์œผ๋‚˜, ์ด ๋ฐฉ๋ฒ•์€ ํ•˜๋‚˜์˜ ์„ค๊ณ„ํ•˜์ค‘ ์กฐ๊ฑด์— ๋Œ€ํ•ด์„œ๋„ ์ˆ˜์ฐจ๋ก€์˜ ๋ฐ˜๋ณต์ ์ธ 3์ฐจ์› ๊ณ ์ฒด ๋ฐ ํŠธ๋Ÿฌ์Šค ์œ ํ•œ์š”์†Œํ•ด์„ ๊ณผ์ •๊ณผ ์œ ํ•œ์š”์†Œํ•ด์„ ๊ฒฐ๊ณผ๋ฅผ ์‘์šฉํ•œ ๋ณต์žกํ•œ ์ˆ˜์น˜์ฒ˜๋ฆฌ ๊ณผ์ •์„ ๊ฑฐ์ณ์•ผํ•˜๋Š” ๋‹จ์ ์œผ๋กœ ์ธํ•ด ์‹ค๋ฌด์ ์šฉ์ด ์–ด๋ ต๋‹ค. ์ด ์—ฐ๊ตฌ์—์„œ๋Š” ๊ธฐ ์ œ์•ˆ๋œ ์ˆ˜์น˜ํ•ด์„์  ๊ธฐ๋ฒ•์„ ์ด์šฉํ•˜์—ฌ ๊ธฐ๋‘ฅ์˜ ์ถ•ํ•˜์ค‘์ด ์ง€๋ฐฐ์ ์ด๋ฉฐ ๊ธฐ๋‘ฅ์ „๋ฉด์—์„œ ํŒŒ์ผ ์ค‘์‹ฌ๊นŒ์ง€์˜ ๊ฑฐ๋ฆฌ์™€ ํŒŒ์ผ์บก์˜ ์œ ํšจ๊นŠ์ด์˜ ๋น„๊ฐ€ 1.0 ๋ฏธ๋งŒ์ด๊ณ  ๊ธฐ๋‘ฅํญ/์œ ํšจ๊นŠ์ด์˜ ๋น„๊ฐ€ 2.0 ๋ฏธ๋งŒ์ธ ๋‹ค์–‘ํ•œ ์„ค๊ณ„์กฐ๊ฑด์„ ๊ฐ–๋Š” Four-pile Cap์˜ ์‹ค์šฉ์ ์ด๊ณ  ํšจ๊ณผ์ ์ธ 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด๋ชจ๋ธ ํ•ด์„/์„ค๊ณ„๋ฅผ ์œ„ํ•œ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ์‹์„ ๊ฐœ๋ฐœ, ์ œ์•ˆํ•˜์˜€๋‹ค.

์ด ์—ฐ๊ตฌ์—์„œ ์ œ์•ˆํ•œ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ์‹๊ณผ ํ˜„ํ–‰ ์„ค๊ณ„๊ธฐ์ค€์˜ ์œ ํšจ๊ฐ•๋„ ์‹๋“ค์„ 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ ํ•ด์„์— ์ ์šฉํ•˜์—ฌ ํŒŒ๊ดด์‹คํ—˜์ด ์ˆ˜ํ–‰๋œ 115๊ฐœ ํŒŒ์ผ์บก์˜ ํŒŒ๊ดด๊ฐ•๋„๋ฅผ ์˜ˆ์ธกํ•˜์˜€๋‹ค. EC2, FIB, ACI 318, AASHTO ์„ค๊ณ„๊ธฐ์ค€์˜ ์ŠคํŠธ๋Ÿฟ ์œ ํšจ๊ฐ•๋„ ์‹๋“ค์— ์˜ํ•œ ํŒŒ์ผ์บก์˜ ์‹คํ—˜ํŒŒ๊ดด๊ฐ•๋„/์˜ˆ์ธก๊ฐ•๋„ ๋น„(ํ‘œ์ค€ํŽธ์ฐจ, ๋ณ€๋™๊ณ„์ˆ˜)์˜ ๋ฒ”์œ„๋Š” 1.43-1.77 (0.611-0.899, 42.7-50.8 %)์ด์—ˆ์œผ๋‚˜, ์ด ์—ฐ๊ตฌ์˜ ์ œ์•ˆ์‹์— ์˜ํ•œ ๊ฐ•๋„์˜ˆ์ธก ๊ฒฐ๊ณผ ๊ฐ’์€ 1.19(0.167, 14.1 %)๋กœ ๋‚˜ํƒ€๋‚˜, ์ด ์—ฐ๊ตฌ์—์„œ ์ œ์•ˆํ•œ ์ŠคํŠธ๋Ÿฟ ์œ ํšจ๊ฐ•๋„ ์‹์€ ํŒŒ์ผ์บก์˜ ๋ชจ๋“  ์„ค๊ณ„๋ณ€์ˆ˜์˜ ๋ฒ”์œ„ ๋ฐ ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ ํ˜•์ƒ์˜ ๋ณ€ํ™”์™€ ๋ฌด๊ด€ํ•˜๊ฒŒ ํŒŒ์ผ์บก์˜ ํŒŒ๊ดด๊ฐ•๋„๋ฅผ ํ˜„ํ–‰ ์„ธ๊ณ„ ์ฃผ์š”์„ค๊ณ„๊ธฐ์ค€์˜ ๊ฒƒ์— ๋น„ํ•ด ๋” ์ •ํ™•ํ•˜๊ณ  ์ผ๊ด€์„ฑ ์žˆ๊ฒŒ ์˜ˆ์ธกํ•˜์˜€๋‹ค. ๋”ฐ๋ผ์„œ ์ด ์—ฐ๊ตฌ์—์„œ ์ œ์•ˆํ•œ ์ŠคํŠธ๋Ÿฟ์˜ ์œ ํšจ๊ฐ•๋„ ์‹์€ Four-pile Cap์˜ 3์ฐจ์› ์ŠคํŠธ๋Ÿฟ-ํƒ€์ด ๋ชจ๋ธ ํ•ด์„ ๋ฐ ์„ค๊ณ„ ์‹œ ๊ทธ ๊ฒฐ๊ณผ์˜ ์‹ ๋ขฐ์„ฑ์„ ๋ณด๋‹ค ํ–ฅ์ƒ์‹œํ‚ฌ ๊ฒƒ์œผ๋กœ ํŒ๋‹จ๋œ๋‹ค.

๊ฐ์‚ฌ์˜ ๊ธ€

์ด ๋…ผ๋ฌธ์€ 2018๋…„๋„ ์ •๋ถ€(๊ต์œก๊ณผํ•™๊ธฐ์ˆ ๋ถ€)์˜ ์žฌ์›์œผ๋กœ ํ•œ๊ตญ์—ฐ๊ตฌ์žฌ๋‹จ์˜ ๊ธฐ์ดˆ์—ฐ๊ตฌ์‚ฌ์—… ์ง€์›์„ ๋ฐ›์•„ ์ˆ˜ํ–‰๋œ ๊ฒƒ์ž„(2018R1D1A1B-06041177).

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